Fifty shades of integration?

Calculus Level 5

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

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