Have Time for Cube Roots?

Algebra Level 4

If f(x)=1x2+2x+13+x2+x3+x23f(x) = \frac { 1 }{ \sqrt [ 3 ]{ { x }^{ 2 }+2x+1 } +\sqrt [ 3 ]{ { x }^{ 2 }+x } +\sqrt [ 3 ]{ { x }^{ 2 } } }

Evaluate n=12196f(n)\displaystyle \sum_{n=1}^{2196} f(n)

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