Can be written as \(\frac{A}{B}\), where \(A\) and \(B\) are not coprime?!

The sum of the reciprocals of all numbers that have a prime factorization of \(A^m B^n\), where \(m\) and \(n\) are positive integers and \(A\) and \(B\) are positive integers that are not necessarily coprime can be expressed as \(\dfrac{A}{B}\). What is \(A+B\)?


Inspiration: Mind your 3's and 2's.

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