A beautiful question

Algebra Level 4

Find the coefficient of the term independent of x in the expansion of \[\Big(\frac{x + 1}{x^{\frac{2}{3}} - x^{\frac{1}{3}} + 1} - \frac{x - 1}{x - x^{\frac{1}{2}}}\Big)^{10}\]

This question was asked in IIT Examination

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