Infinite Sum of an Infinite Sum of an Infinite Sum

Calculus Level 4

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

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

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