Easy squeezy

Algebra Level pending

\[\large \sum_{m=1}^\infty \sum_{n=1}^\infty \frac{m^2n}{3^m(n3^m+m3^n)} \]

If the above summation can be expressed as \(\dfrac{a}{b}\), where \(a\) and \(b\) are coprimes, then find \(a+b\).

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