Boxes sliding down the plank !!!

On a winter day, Cody is shoving boxes up a rough plank inclined at an angle $30°$ . The plank is partially covered with ice , with more ice near the bottom of the plank than near the top, so that the coefficient of friction increases with the distance $x$ along the plank : $\mu=2x$ and at the bottom of the plank, $x=0$ ,(For this plank, coefficient of Kinetic and Static friction are equal). Cody shoves a box up the plank so that it leaves the bottom of the plank moving with speed $v$ . The minimum possible value of $v$ such that the box comes to rest after losing its kinetic energy to friction is $\frac{a}{b}\sqrt{g}$ . Find the value of $a+b$

Here $g$ is accleration due to gravity