Soviet Trig Eqn. 1

Geometry Level 5

Solve, for \( 0^{\circ} < x < 90^{\circ}\), the following equation for \(x\):

\[ \sqrt{13-12\cos x}+\sqrt{7-4\sqrt{3}\sin x}=2\sqrt{3} \]

If \(x\) can be represented in the form \( \arccos\left( \dfrac{a+\sqrt{b}}{c}\right)\), find \(a+b+c\).

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