A separable equation

Calculus Level 2

If \(\dfrac{dy}{dx}=e^{x+y}\), and \(y(0)=0\), then the value of \(y(-\ln 2)\) can be written in the form \(\ln \left(\dfrac mn\right)\), where \(m\) and \(n\) are coprime positive integers. Find \(m+n\).