Find the value of the base $b$ such that the following addition problem is correct: $$ \begin{array}{@{}c@{\;}c@{}c@{}c@{}c@{}c} & & 6 & 6 & 5 & 1_b \\ + & & & 1 & 1 & 5_b \\ \cline{1-6} & 1 & 0 & 0 & 6 & 6_b\\ \end{array} $$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the value of the base $b$ such that the following addition problem is correct: $$ \begin{array}{@{}c@{\;}c@{}c@{}c@{}c@{}c} & & 6 & 6 & 5 & 1_b \\ + & & & 1 & 1 & 5_b \\ \cline{1-6} & 1 & 0 & 0 & 6 & 6_b\\ \end{array} $$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
7
Find the value of the base $b$ such that the following addition problem is correct: $$ \begin{array}{@{}c@{\;}c@{}c@{}c@{}c@{}c} & & 6 & 6 & 5 & 1_b \\ + & & & 1 & 1 & 5_b \\ \cline{1-6} & 1 & 0 & 0 & 6 & 6_b\\ \end{array} $$
train