The sum of all local minimum values of the function
$f(x) = \left\{ {\begin{array}{*{20}{c}}
{1 - 2x,}&{x < - 1}\\ {\frac{1}{3}(7 + 2|x|),}&{ - 1 \le x \le 2}\\ {\frac{{11}}{{18}}(x - 4)(x - 5),}&{x > 2}
\end{array}} \right.$
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