The symbolism $\lfloor x\rfloor$ denotes the largest integer not exceeding $x$. For example, $\lfloor 3\rfloor =3$, and $\lfloor 9/2\rfloor =4$. Compute $\lfloor \sqrt[3]{1}\rfloor +\lfloor \sqrt[3]{2}\rfloor +\lfloor \sqrt[3]{3}\rfloor +\cdots +\lfloor \sqrt[3]{30}\rfloor$.