Let A=(0,0) and B=(b, 2) be points on the coordinate plane. Let A B C D E F be a convex equilateral hexagon such that \angle F A B=120^{\circ}, \overline{A B}\|\overline{D E}, \overline{B C}\| \overline{E F}, \overline{C D} \| \overline{F A}, and the y-coordinates of its vertices are distinct elements of the set \{0,2,4,6,8,10\}. The area of the hexagon can be written in the form m \sqrt{n}, where m and n are positive integers and n is not divisible by the square of any prime. Find m+n.