I like integrals 2

Calculus Level 4

\[ \large \int_0^1 \dfrac{\ln(1-x) }{e^x} \, dx = - \dfrac A{B e} \sum_{n=1}^\infty \dfrac1{n \cdot n!} \]

If the equation above holds true for positive integers \(A\) and \(B\), where \(A\) and \(B\) are coprime positive integers, find \(A+B\).

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