A normal tangent

Calculus Level 4

If the tangent at the point \( (4m^2 , 8m^3 ) \), where \(m > 0\) is a parameter, to the curve \( \displaystyle x^3 = y^2 \) is normal to it again at some point, then the value of \(m\) can be expressed as \( \displaystyle \frac{\sqrt{a}}{b} \), where \(a\) is square-free.

Enter the value of \(a+b\).

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