Floor Ceiling Ceiling Floor: JEE Style
\[ \large \lceil x \lfloor x \rfloor \rceil + \lfloor x \lceil x \rceil \rfloor = 1729 \]
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.