Let's go up a floor

Algebra Level 4

$\large \left\lfloor \sum_{x=1}^\infty \dfrac1{x^2} + \sum_{x=1}^\infty \dfrac1{3^x} \right \rfloor = \sum_{x=2}^\infty \dfrac{n}{x^2} + \sum_{x=2}^\infty \dfrac n{4^x}$

The equation above has a real solution $$n$$, which can be expressed in the form $$n=\frac { C }{ A{ \pi }^{ A }-B }$$. If $$A$$, $$B$$, and $$C$$ are positive integers, find $$A+B+C$$.

Picture credits: HK Bank of China Tower by WiNG, Wikipedia

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