If only it's a power of 3

Geometry Level 5

\[\large 2\sqrt[3]{3\sec ^2 20^\circ \sin^2 10^\circ}\]

The expression above can be expressed in the form \(a+b\sec 20^\circ\), where \(a\) and \(b\) are integers. What is the value of \(a+b\)?

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