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

\[ \sqrt{2-2\cos x}+\sqrt{10-6\cos x}=\sqrt{10-6\cos 2x} \]

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

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