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$\large \int_{-1/\sqrt{3}}^{1/\sqrt{3}} \dfrac{x^2(1-x^2)}{(e^x+1)(1+x^2)^4} \, dx$

If the above integral is equal to $\dfrac{\sqrt{a}}{b}$, where $a$ and $b$ are positive integers with $a$ square-free, find $a+b$.

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