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Math·Advanced Math·Nonlinear functions

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The function $f$ is defined by $f(x)=\frac{x^2+ax+b}{2x+c}$, where $a$, $b$, and $c$ are constants. The graph of the function $f$ in the xy-plane, where $y=f(x)$, does not intersect the line $x=4$. If $f(5)=f(6)=0$, what is the value of $a+b+c$?

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