\[ \large \lceil x \lfloor x \rfloor \rceil + \lfloor x \lceil x \rceil \rfloor = 1729 \]

If the range of positive \(x\) satisfy the equation above is \( \alpha \leq x \leq \beta \).

What is the value of \(30\alpha + 29 \beta+1\) if we know that it is an integer?

Inspired by: Floor Ceiling Ceiling Floor.

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