Find regular expression for a given language $L=\{0^{n}1^{m}\,\,\,|\,\,\,n+m(mod3)\neq0\}$

Question

Question.

Write a regular expression for the language: $L=\{0^{n}1^{m}\,\,\,|\,\,\,n+m(mod3)\neq0\}$

Attempt.

$r=(000)^* (0(ε+0+1+011)+1(ε+1)) (111)^*$

Is my regular expression correct? If so, is there a shorter expression ?