For \( a, b \in \mathbb{Z} \) and \( |a-b| \leq 10 \), let the angle between the plane \( P: ax + y - z = b \) and the line \( l: x - 1 = a - y = z + 1 \) be \( \cos^{-1}\!\left(\dfrac{1}{3}\right) \). 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:
