Allen and Bethany each arrive at a party at a random time between 1:00 and 2:00.  Each stays for 15 minutes, then leaves.  What is the probability that Allen and Bethany see each other at the party?The answer is in the form rac{m}{n}, where gcd(m, n) = 1. Please provide the value of m + n.

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