Intersection between a function and it's NOT derivative

A function, $f(x)=(x-1)(x-3)(x-5)$ is plotted. Then, another function, $f'(x)+26x$ is plotted, to find the intersection point of the two functions. Given that the x-coordinate of the only one intersection point can be written in the form of $\sqrt[3]{a+\sqrt b} - \sqrt[3]{-a+\sqrt b} + c$ , find the last three digits of $a+b+c$ .