A Dubicious Recursion?

\[\begin{align*}x_{1}&=211,\\ x_{2}&=375,\\ x_{3}&=420,\\ x_{4}&=523,\ \text{and}\\ x_{n}&=x_{n-1}-x_{n-2}+x_{n-3}-x_{n-4}\ \text{when}\ n\geq5, \end{align*}\]

Given the recurrence relation above, find the value of \(x_{531}+x_{753}+x_{975}\).

This an old Olympiad problem.
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