Freddy's answer is almost correct. The problem is really in the signature of LoadFile(). It probably should not be taking a char* argument. It should probably be taking a const char* argument. Are you planning on modifying the passed in string into LoadFile()? If not, make it const if the source is under your control--and if you won't break too many things.
In reality, you would have to do this:
CString filename("somefile.txt");
LoadFile((LPSTR)(LPCSTR) filename); // need the extra cast to (LPSTR)
or
LoadFile((LPSTR) filename.GetString());
This is all assuming you aren't building for Unicode. If you are building for Unicode, it's going to be different.
If you were building for Unicode, I would have changed the function signature to:
void LoadFile(LPCTSTR szFileName); // LPCTSTR == const TCHAR* (TCHAR is char for MBCS and wchar_t for Unicode)