Elisa swims laps in the pool. When she first started, she completed $10$ laps in $25$ minutes. Now, she can finish $12$ laps in $24$ minutes. By how many minutes has she improved her lap time? Provide your answer in the form of a simplified fraction \(\frac{k}{m}\), and calculate the value of \(k + m\).

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