Solve for $x$. \[ \begin{array}{l} \sqrt[3]{3 x-4}=3 \\ x= \end{array} \]

Step 1 ：\((\sqrt[3]{3x-4})^3 = 3^3\)

Step 2 ：\(3x - 4 = 27\)

Step 3 ：\(3x = 27 + 4\)

Step 4 ：\(3x = 31\)

Step 5 ：\(x = \frac{31}{3}\)

Step 6 ：\(\sqrt[3]{3(\frac{31}{3})-4} = 3\)

Step 7 ：\(\sqrt[3]{31-4} = 3\)

Step 8 ：\(\sqrt[3]{27} = 3\)

Step 9 ：\(\boxed{x = \frac{31}{3}}\)