Again a Complex Number System

Algebra Level 5

Let \(a, b, c\) be complex numbers satisfying \[a + b +c = abc = 1\]

and \[\dfrac{ab+bc+ac}{3} = \dfrac{1}{a^2}+\dfrac{1}{b^2}+\dfrac{1}{c^2}\]

The sum of absolute values of all possible \(ab + ac + bc\) can be written as \(\dfrac{\sqrt{n}}{m}\) , where \(n\) and \(m\) are positive coprime integers. What is the value of \(n + m\) ?

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