BD-BDMO 2022 Problem 1

Find all solutions for real $x$ , $\lfloor x\rfloor^3 -7 \lfloor x+\frac{1}{3} \rfloor=-13.$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.