\[\left(\dfrac{1}{1+2ab-c^2}+\dfrac{1}{1+2bc-a^2}+\dfrac{1}{1+2ca-b^2}\right)^2\]

Let \(a,b\) and \(c\) be non-negative real numbers such that \(a^2+b^2+c^2=1\).

The minimum value of the expression above can be expressed as \(\dfrac{p}{q}\) for positive coprime integers \(p,q\). Find \(p+q\).

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