Too Difficult? 3

Calculus Level 3

$\large \int_{1/4}^{1/12} \dfrac{ -x}{4x\sqrt{x^3} + \sqrt{x^3}} \, dx$

The integral above is equal to $$\dfrac ab \pi$$, where $$a$$ and $$b$$ are coprime positive integers, find $$a+b$$.

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