\[ \large \int \frac{e^x + e^{-x} - 1}{(e^x \sin x + \cos x)(\cos x - \sin x e^{-x} ) } \, dx \]

If the indefinite integral above is of the form \[ \ln \left | \dfrac{e^x \sin x + A\cos x}{e^x \cos x + B\sin x}\right | + C, \]

where \(A\) and \(B\) are constants and \(C\) is the arbitrary constant of integration, what is the value of \(A+ B?\)

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