In the $xy$-plane, a circle of radius $4$ with center on the positive $x$-axis is tangent to the $y$-axis at the origin, and a circle with radius $10$ with center on the positive $y$-axis is tangent to the $x$-axis at the origin. Find the slope of the line passing through the two points at which these circles intersect. The original answer is in \(\frac{k}{m}\) format, please give the value of k + m.

Let's think step by step and output the final answer within \boxed{}.
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