A game of solitaire is played as follows. After each play, according to the outcome, the player receives either $a$ or $b$ points ( $a$ and $b$ are positive integers with $a$ greater than $b$ ), and his score accumulates from play to play. It has been noticed that there are thirty-five non-attainable scores and that one of these is 58. Find the sum of $a$ and $b$. 

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