Floor Ceiling Ceiling Floor

Algebra Level 4

If the range of positive \(x\) satisfy the equation \( \lceil x \lfloor x \rfloor \rceil + \lfloor x \lceil x \rceil \rfloor = 111 \) is \( \alpha \leq x \leq \beta \). What is the value of \(8\alpha + 7 \beta\)?

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