Radically Remarkable Root

Algebra Level 5

\[\large 6x^3-3x^2-6x-4=0\]

The real root to the equation above can be written in the form \(\large \dfrac{\sqrt[3]{a}+\sqrt[3]{b}+1}{c}\), where \(a\), \(b\) and \(c\) are positive integers.

Find \(a+b+c\).

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