\[\large \int_{-1}^1 \dfrac{\partial}{\partial x} \left(\dfrac1{1+e^\frac1x}\right)~dx\]

If the above integral can be expressed as \(\dfrac {A+Be}{C+De^E}\), where \(A\), \(B\), \(C\), \(D\) and \(E\) are integers, with least values, also \(A>0\) and \(e\) is the Napier's constant. Find \(A+B+C+D+E\)

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