Alternatively, you could use trail and error. So:
$${{\mathtt{1}}}^{{\mathtt{3}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{2}}}^{{\mathtt{3}}} = {\mathtt{9}}$$
Too low
$${{\mathtt{3}}}^{{\mathtt{3}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{4}}}^{{\mathtt{3}}} = {\mathtt{91}}$$
Still too low
$${{\mathtt{6}}}^{{\mathtt{3}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{7}}}^{{\mathtt{3}}} = {\mathtt{559}}$$
Too high
$${{\mathtt{5}}}^{{\mathtt{3}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{6}}}^{{\mathtt{3}}} = {\mathtt{341}}$$
Bingo