A fixed solid sphere with radius \(R\) and charge density given by \(\rho (r) = \dfrac{\rho_{0}}{r^2}\) is placed at a distance \(2d\) from a fixed particle with charge \(q\) (from the center of the sphere). If at a distance \(x\) from the fixed particle there is a point charge at equilibrium, then \(x\) can be written as \[\dfrac{ad\sqrt{q}}{b\sqrt{\pi R \rho_{0}}+\sqrt{q}}.\]

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

Assume both of the fixed charges are of the same sign.

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