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Algebra Level 4

α6+β6+γ6+(αβ)3+(βγ)3+(αγ)3 \large\alpha^6 + \beta^6 + \gamma^6 + (\alpha\beta)^3 + (\beta\gamma)^3 + (\alpha\gamma)^3

Let α,β\alpha, \beta and γ \gamma be the zeroes of the polynomial x3x1x^3-x-1. Find the value of the expression above.

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