Revisiting familiar triangles

Geometry Level 5

$\large \sqrt{5-4\cos(x)} + \sqrt{13-12\sin(x)} = \sqrt{10}$

If $$x$$ is a positive acute angle that satisfies the equation above, and can be represented in the form of $$\cos^{-1} \left( \dfrac{a-\sqrt b}c \right)$$ for positive integers $$a,b$$ and $$c$$ with $$b$$ square-free, find the value of $$a+b+c$$.

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