Declining to insanity in 2017!

Algebra Level 4

\[\large{405f(x) = \sqrt[x]{\sum_{k=1}^{2017}\sum_{i=1}^{3}{k^i}}}\] Find the smallest positive integer \({C}\) such that \( \left \lfloor {f\left(\frac{10}{7}\right)}\right \rceil\) \(+C\) is a palindrome.

\(\)
Notation: \( \lfloor \cdot \rceil \) denotes the nearest integer function.

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