Json.Net serialize/deserialize dictionary class member with custom key type

Question

I have a problem trying to properly serialize/deserialize object with inner dictionary. Dictionary has some custom type PairIntKey as a key.

Code is the following:

public class MyClassWithDictionary
    {
        private Dictionary<PairIntKey, List<int>> _myDictionary = new Dictionary<PairIntKey, List<int>>();

        public Dictionary<PairIntKey, List<int>> MyDictionary
        {
            set { _myDictionary = value; }
        }

        public void AddElementsToMyDictionary(PairIntKey key, List<int> value)
        {
            _myDictionary.Add(key, value);
        }
    }

    public class PairIntKey : IEquatable<PairIntKey>
    {
        private int _value1;

        private int _value2;

        public int Value1
        {
            get { return _value1; }
        }

        public int Value2
        {
            get { return _value2; }
        }

        public PairIntKey(int value1, int value2)
        {
            _value1 = value1;
            _value2 = value2;
        }

        public override int GetHashCode()
        {
            return _value1 + 29 * _value2;
        }

        public bool Equals(PairIntKey other)
        {
            if (this == other) return true;
            if (other == null) return false;
            if (_value1 != other._value1) return false;
            if (_value2 != other._value2) return false;
            return true;
        }

        public override string ToString()
        {
            return String.Format("({0},{1})", _value1, _value2);
        }

    }

I serialize like this

public void SerializeAndDeserializeMyObject()
        {
            var myObject = new MyClassWithDictionary();
            myObject.AddElementsToMyDictionary(new PairIntKey(1, 1), new List<int> {5});

            var contractResolver = new DefaultContractResolver();
            contractResolver.DefaultMembersSearchFlags |= BindingFlags.NonPublic;

            string serializedItem = JsonConvert.SerializeObject(myObject,
                                                                Formatting.Indented,
                                                                new JsonSerializerSettings()
                                                                    {
                                                                        ContractResolver = contractResolver,

                                                                    });

            var deserializedItem = JsonConvert.DeserializeObject(serializedItem, typeof(MyClassWithDictionary),                                                                 new JsonSerializerSettings()
                                                                    {
                                                                        ContractResolver = contractResolver,

                                                                    });


            }

serializedItem looks like

{
  "_myDictionary": {
    "(1,1)": [
      5
    ]
  }
}

The problem is that deserializedItem has empty MyDictionary member. Its pretty obvious as soon as Json.Net doesn't know how to convert string "(1,1)" into PairIntKey class instance. How to do a proper converter for that case? Or it should not be a converter?