Not too hard I

Algebra Level 5

Let \(a\), \(b\) anc \(c\) be complex numbers such that:

\[a^2+b^2+c^2=14\\ a^3+b^3+c^3=20\\ ab+ac+bc=-5\]

Let \(A\) the sum of all possible values of \(|(a-b)(a-c)(b-c)|\). If \(A=\dfrac{m+2\sqrt{n}}{3}\), find \(m+n\).

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