Find the value of \(x\)

Geometry Level 3

\[\large \sin 20^\circ \cos 50^\circ = x \sec 10^\circ\] If the real number \(x\) satisfying the above equation is of the form \(\dfrac {\sqrt {a}}{b}\), where \(a\) and \(b\) are integers, and \(a\) is square-free, find \(a+b\).

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