Let \( \alpha, \beta, \gamma \) be the roots of the equaiton \(z^3= 1 \) such that \( \beta \) is in the form \( \frac { -a + i \sqrt b }{c} \) where \(a,b,c \) are positive integers and \(\gamma \) as the conjugate of \(\beta \).

Given that \(x = \beta - \gamma - \alpha - 1 \). Find the value of \(x^4 + 3x^3 + 2x^2 - 11x - 6 \).

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