Let \ell_1 and \ell_2 be two parallel lines, a distance of 15 apart. Points A and B lie on \ell_1 while points C and D lie on \ell_2 such that \angle BAC = 30^\circ and \angle ABD = 60^\circ. The minimum value of AD + BC is a\sqrt{b}, where a and b are integers and b is squarefree. Find a + b.