Joel is rolling a 6-sided die. After his first roll, he can choose to re-roll the die up to 2 more times. If he rerolls strategically to maximize the expected value of the final value the die lands on, the expected value of the final value the die lands on can be expressed as $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. What is $m+n$?

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