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 $a+b+c$ .