VTMO 2019 — Grade 9 — final Question 2

$a$)For real $a , b$ with a $^{3} + b^{3} + 6 ab = 8$, find $a + b$. $b$)Find real a such that $a + 3 \sqrt{11}$ and $\frac{1}{a} - 3 \sqrt{11}$ are integers.