Let \( H_n = 1+\dfrac12 + \dfrac13 + \cdots + \dfrac1{n}\) be the \(n^\text{th}\) harmonic number.

The sum \[\sum_{n=1}^\infty \frac{H_n}{n2^n} = \dfrac{\pi^{A}}{B} \] for some positive integers \( A\) and \(B\). What is \( A+B\)?

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