Find the largest value of $t$ such that \[\frac{13t^2 - 34t + 12}{3t - 2 } + 5t = 6t - 1.\]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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