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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