Infinite Sum of an Infinite Sum of an Infinite Sum

Calculus Level 3

$\large{A=\displaystyle \sum_{x=2}^{\infty} \displaystyle \sum_{n=1}^{\infty} \displaystyle \sum_{k=1}^{\infty} \dfrac{1}{x^nx^k}}$

If $$A=\cfrac{\pi^m}{n}$$ for positive integers $$m$$ and $$n$$, find the value of $$m+n$$.

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