Consider real numbers $A$, $B$, \dots, $Z$ such that:
\[ 
  EVIL = \frac{5}{31}, \; 
  LOVE = \frac{6}{29}, \text{ and } 
  IMO  = \frac{7}{3}. 
\] 
If $OMO = \frac{m}{n}$ for relatively prime positive integers $m$ and $n$, find the value of $m+n$.

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