Fifty shades of integration?

Calculus Level 4

\[ \large \displaystyle \large \int_{0}^{1} x^{2} (1-x)^4 \ln \left(\frac{1}{x}\right ) \, dx \]

If the value of the integral above is equal to \( \dfrac ab\), where \(a\) and \(b\) are coprime positive integers, find \(a+b\).

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