Too Difficult? 3

Calculus Level 4

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

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

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