Vieta's might come in handy (Polynomials Sprint question)

Algebra Level 2

The roots of the equation

$6x^3 - 3x^2 +2x - 1 = 0,$

are $$\alpha, \beta$$ and $$\gamma$$. Find the value of

$1 + \alpha + \beta + \gamma + \alpha \beta + \beta \gamma + \gamma \alpha + \alpha \beta \gamma.$

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