In a middle-school mentoring program, a number of the sixth graders are paired with a ninth-grade student as a buddy. No ninth grader is assigned more than one sixth-grade buddy. If $\frac{1}{3}$ of all the ninth graders are paired with $\frac{2}{5}$ of all the sixth graders, find the fraction of the total number of sixth and ninth graders that have a buddy. 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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