Again a Complex Number System

Algebra Level 5

Let a,b,ca, b, c be complex numbers satisfying a+b+c=abc=1a + b +c = abc = 1

and ab+bc+ac3=1a2+1b2+1c2\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+bcab + ac + bc can be written as nm\dfrac{\sqrt{n}}{m} , where nn and mm are positive coprime integers. What is the value of n+mn + m ?

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