Three balls having masses \(2m\), \(3m\) and \(5m\) having equal velocities \(v_0\) collide with a block of wood of mass \(6m\) which is at rest, in a perfectly elastic collision.

Now, this whole system of the balls and the block is moving with a velocity of \(v_1\).

If the ratio \(\dfrac{v_0}{v_1}\) is equal to \(\dfrac ab\), where \(a\) and \(b\) are co-prime, find \(a+b\).

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