Circles \mathcal{C}_{1} and \mathcal{C}_{2} intersect at two points, one of which is (9,6), and the product of their radii is 68. The x-axis and the line y=m x, where m>0, are tangent to both circles. It is given that m can be written in the form a \sqrt{b} / c, where a, b, and c are positive integers, b is not divisible by the square of any prime, and a and c are relatively prime. Find a+b+c.