Consider an arithmetic sequence where the first term is \( a_1 \) and the common difference is \( d \). The sequence has 5 terms: \( a_1, a_2, a_3, a_4, a_5 \). If the probability that a randomly selected term from this sequence satisfies the polynomial equation \( x^2 - 11x + 24 = 0 \) is \( \frac{m}{n} \), where \( m \) and \( n \) are relatively prime positive integers, find the value of \( m + n \). Let's think step by step and output the final answer within \boxed{}.
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