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Algebra Level 4

Given the equation

\[ x \lfloor x \lfloor x \lfloor x \rfloor \rfloor \rfloor = 41 \]

If \(\alpha \) denote the largest negative value of \(x\) which satisfy the equation above, while \(\beta\) denote the smallest positive value of \(x\) which satisfy the equation above.

What is the value of \(17\alpha + 28\beta \)?

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