It is not hard as it looks!

Algebra Level 4

$\large\alpha^6 + \beta^6 + \gamma^6 + (\alpha\beta)^3 + (\beta\gamma)^3 + (\alpha\gamma)^3$

Let $\alpha, \beta$ and $\gamma$ be the zeroes of the polynomial $x^3-x-1$ . Find the value of the expression above.