Edge Case Of Rolling!

On the edge of a cuboidal plank of mass $M = 8\text{ kg}$, a uniform solid spherical ball of mass $m = 12\text{ kg}$ and radius $R$ is kept. The ball is given a very slight push towards right. There is $\underline{\text{no}}$ friction between plank and ground and friction between ball and plank is sufficient to $\underline{\text{prevent slipping}}$. The plank won't topple during the journey.

If when ball just loses contact with plank, the angle made by Center of Mass ball with vertical is $\theta$, then $\displaystyle \cos\theta = \frac{\sqrt{a} - b}{3} \text{ where } a, b \in I^+$ Enter your answer as $a + b$.

Inspiration Aniket Sanghi

All of my problems are original.