What is the value of

\(\left(\left((2+1)^{-1}+1\right)^{-1}+1\right)^{-1}+1?\)

Provide your answer in the form of \(\frac{k}{m}\), where the fraction is in the simplest form. Calculate the value of \(k + m\).

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