\[\large \int \dfrac{\sin^2x \cos^2x }{(\sin^3x+\cos^3x)^2} \, dx \]

The indefinite integral above is equal to

\[ -\dfrac{1}{3}\frac{\cos^3 x}{(A\cos x+B\sin x)(1-\sin x \cos x)}+C\]

for constants \(A\) and \(B\), where \(C\) denotes the arbitrary constant of integration. Find the value of \(A+B\).

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