The xenial-cran35/
version of the repo does NOT work if you have a "default release" set in apt, as is the case in some distros that work on top of Ubuntu, such as Mint. For my Mint distro, there exists a file /etc/apt/apt.conf.d/01ubuntu
inside of which it declares the Default-Release "xenial";
What this means is that, since r-base exists in the ubuntu repo at version 3.2, with release "xenial", it'll never use the 3.6 branch from the other repo, because the release name for that repo is "xenial-cran35". You need to edit that file to change the default release to "xenail-cran35", or do something more pointed using apt preference files (https://wiki.debian.org/AptPreferences#A.2Fetc.2Fapt.2Fpreferences).
This is basically R's fault for having a poorly formatted repo. They should have had 2 repos, each of which had a "xenial" release folder, one url for their 3.2 branch work and one for the 3.5+ branch work. Instead they have one repo, and have bastardized the "release name" instead, which just sort of happens to work for base Ubuntu, but won't work if you have non-base configuration of apt in this way.