Let $f$ be a function for which $f\left(\dfrac{x}{3}\right) = x^2 + x + 1$. Find the sum of all values of $z$ for which $f(3z) = 7$. The original answer is in the form of $-\frac{k}{m}$, where $k$ and $m$ are integers. Please give the value of $k + m$.

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