I think when you say "any more", it has something to do with 'quantity' or perhaps, a 'I donstate of 'presence' as opposed to "any longer" which merely describe 'duration' or 'time'.
'I don't have money any more.' (it implies that you have lots of money before but it's gone now.)
'I don't live there any longer.' (it means that you had been living in that place for quite some time.)
these two however can sometimes be interchangeable, like in the case of the 2nd sentence "I don't live there any more."
you just have to research for these two phrases where and when to use them correctly and be familiarized of it:
"you don't love me any more."
"you don'tlove me any longer"
although the above sentences are both valid, the first one would seem natural and very common to hear.