# Roots of Cubic Equation

Algebra Level 5

For a real number $$k$$, the cubic equation $$\frac{1}{3}x^3-x=k$$ has three distinct roots $$\alpha, \beta$$ and $$\gamma$$. If $m=\min_{k\in \mathbb{R}}(|\alpha|+|\beta|+|\gamma|),$ what is $$m^2?$$

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