\[\large{L=\lim_{n \to \infty} \int_{-n}^{n} \dfrac{dx}{(x^2+1)(e^x+1)}}\]

If \(L\) can be expressed as \({\dfrac{\pi^A}{B}}\) where \(A,B\) are positive integers, then find the value of \(A+B\).

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