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A cubic polynomial
f(x)=8x3−3x2−3x−1 f(x) = 8x^3-3x^2-3x-1f(x)=8x3−3x2−3x−1
has one real root of the form a3+b3+1c \frac{ \sqrt[3]{a} + \sqrt[3]{b} + 1} { c} c3a+3b+1, where a,b,ca, b, ca,b,c are positive integers. Find a+b+c a + b + c a+b+c.
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