Easy squeezy

Algebra Level 4

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

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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