Jim has two fair 6-sided dice: one die has faces labelled from 1 to 6, and the second die has faces labelled from 3 to 8. Twice, he randomly picks one of the dice (each die equally likely) and rolls it. Given that the sum of the resulting two rolls is 9, if \( \frac{m}{n} \) is the probability he rolled the same die twice where \( m, n \) are relatively prime positive integers, then what is \( m + n \)?

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