A Beautiful Integral

Calculus Level 4

\[\large \displaystyle \int_0^1 \dfrac{\ln (1-x) }{x} \, dx\] If the integral above can be expressed as \( -\dfrac AB \pi^C \), where \(A,B\) and \(C\) are positive integers with \(A\), and \(B\) being coprime integers, find \(A+B+C\).