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Algebra Level 5

Today, I went to my grandmother's house to eat some delicious apple pie. However, being mischievous as always, she decided to test me with a question before letting me eat the pie.

xxxx=88 \large \lfloor x \lfloor x \lfloor x \lfloor x \rfloor\rfloor\rfloor\rfloor = 88

If AB\frac AB is the smallest positive value of xx that satisfy the equation above for coprime positive integer AA and BB, what is the value of A+BA+B?

Adapted from a recreational mathematics book.
Image Credit: Flickr Dennis Wilkinson.

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