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Calculus Level 4

\[ \large \int_0^{\pi/4} \sin(x) \cos(3x) \sin(5x) \cos(7x) \sin(9x) \cos(11x) \, dx \]

If the integral above is equal to \( \dfrac ab\), where \(a\) and \(b\) are coprime positive integers, find the value of \(a+b\).

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