Double the sum, double the fun!

Calculus Level 5

Evaluate the following:

\[ \sum_{a=1}^{\infty}\displaystyle\sum_{b=1}^{\infty} \dfrac{6a^2}{b^6+a^4b^2}\]

If the answer can expressed in the form \( \dfrac{\pi^n}{m} \) for positive integers \( n \) and \( m\), find the value of \( n + m \).

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