Intersection between a function and it's NOT derivative

Level pending

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 \(a+b+c\).

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