a trigonometry problem

Geometry Level 4

$\large \cos { (5x) } +\cos { (x) } +2\cos { (3x) } \sin { (2x) } =12\cos { (3x) }$

If the solution of the equation above for $$0<x<\dfrac { \pi }{ 2 }$$ can be written as $$\dfrac { a }{ b } \pi$$, where $$a$$ and $$b$$ are coprime positive integers, find $$a+b$$.

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