Just Minimize the Function!

Algebra Level 3

Let f f be a real function such that f(x)=x2x+13 f(x) = \sqrt[3]{x^2-x+1} for xx is real number. What is the minimum value of the function f f?

If this minimum value can be expressed as bca \sqrt[a]{\dfrac bc} , where a,b,ca,b,c are positive integers, with bb and cc being coprime integers and aa minimized, submit your answer as a+bca+b-c.


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