solution: Since $90^3=729,\!000$, $\text{AB}$ is greater than 90.  Therefore, $\text{A}=9$.  Since the ones digit of $\text{AB}^3$ is 3, $\text{AB}$ must be odd.  The ones digit of $\text{AB}^3$ is the same as the ones digit of $\text{B}^3$, so we look at the ones digits of the cubes of the odd digits. \[
  \begin{array}{c}
  \text{The ones digit of }1^3 \text{ is } 1. \\ \text{The ones digit of }3^3 \text{ is } 7. \\ \text{The ones digit of }5^3 \text{ is } 5. \\ \text{The ones digit of }7^3 \text{ is } 3. \\ \text{The ones digit of }9^3 \text{ is } 9.
  \end{array}
  \] Only $7^3$ has a ones digit of 3, so $\text{B}=7$.  Therefore, $\text{A}+\text{B}=9+7=\boxed{16}$.
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  When the two-digit integer $``\text{AB}"$ is cubed, the value is $912,\!673$. What is $A + B$?
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: 16
extra_info.question: When the two-digit integer $``\text{AB}"$ is cubed, the value is $912,\!673$. What is $A + B$?
extra_info.split: test