Question 155
Let $a$ and $b$ be the two roots of the equation $x^{\frac{4}{3}} - 2022x^{\frac{2}{3}} + 2023 = 0$. If $p = a + 3a^{\frac{1}{3}}b^{\frac{2}{3}}$ and $q = b + 3a^{\frac{2}{3}}b^{\frac{1}{3}}$, find the value of $(p+q)^{\frac{2}{3}} + (p-q)^{\frac{2}{3}}$.