3d Geometry

For \(\mathrm{a}, \mathrm{b} \in \mathbb{Z}\) and \(|\mathrm{a}-\mathrm{b}| \leq 10\), let the angle between the plane \(\mathrm{P}: \mathrm{ax}+y-\mathrm{z}=\mathrm{b}\) and the line \(l: x-1=\mathrm{a}-y=z+1\) be \(\cos ^{-1}\left(\frac{1}{3}\right)\). If the distance of the point \((6,-6,4)\) from the plane P is \(3 \sqrt{6}\), then \(a^{4}+b^{2}\) is equal to :