Roots of Cubic Equation

Algebra Level 5

For a real number kk, the cubic equation 13x3x=k\frac{1}{3}x^3-x=k has three distinct roots α,β\alpha, \beta and γ\gamma. If m=minkR(α+β+γ),m=\min_{k\in \mathbb{R}}(|\alpha|+|\beta|+|\gamma|), what is m2?m^2?

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