Inte-greater!

Calculus Level 4

\[\large \int _{ - \pi / 6 }^{ \pi / 6 }{ \cfrac { \sin x }{ \sin x - \cos x } } \, dx = \, \dfrac{\pi}{A} + \dfrac{1}{2} \, \ln (B-\sqrt C )\]

Given \(A\), \(B\) and \(C\) are positive integers satisfying the equation above, find \(A+B+C\).

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