Polynomial coefficients based off of its roots

Algebra Level 3

If the ordered triple (a, b, c) of integers are the coefficients for \(x^3+ax^2+bx+c=0\). Find the minimum of \(|a+b+c|\) If \(x=\sqrt[3]{2+\sqrt{3}}+\sqrt[3]{2-\sqrt{3}}\)

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