Let $a$ and $b$ be nonzero real numbers such that $\tfrac{1}{3a}+\tfrac{1}{b}=2011$ and $\tfrac{1}{a}+\tfrac{1}{3b}=1$.  What is the quotient when $a+b$ is divided by $ab$?

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