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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