\[ \large \lim_{m\to\infty} \int_{-\infty}^{\infty} \dfrac{dx}{1+x^2+x^4 + \cdots + x^{2m}} \, dx \]

If the limit above can be expressed as \(\dfrac AB\), where \(A\) and \(B\) are coprime positive integers, find \(A+B\).

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