Mathematics Question from JEE Main 2026 · 28 January, Shift 2

Let $f$ be a differentiable function satisfying $f(x)=1-2x+\int_0^x e^{(x-t)}f(t)\,dt,\quad x\in\mathbb{R},$ and let $g(x)=\int_0^x \{f(t)+2\}^{15}(t-4)^6(t+12)^{17}\,dt.$ If $p$ and $q$ are respectively the points of local minima and local maxima of $g$, then the value of $|p+q|$ is _____.