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Calculus Level 5

\[ \large \sum_{n=1}^\infty\dfrac1{64n^2-1} \]

If the series above equals to \( \dfrac1A - \dfrac{1}B\pi \cot\left(\dfrac AB \pi\right) \) for positive integers \(A\) and \(B\), find the value of \(A+B\).

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