This is the graph of $y=\sqrt{6 x+7}$, which goes through (-1,1), (3,5), (5,6), (7,7). Use the graph to find an approximate solution to $\sqrt{6 x+7}=6$. Round your answer to the nearest integer.

Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.
Question: This is the graph of $y=\sqrt{6 x+7}$, which goes through (-1,1), (3,5), (5,6), (7,7). Use the graph to find an approximate solution to $\sqrt{6 x+7}=6$. Round your answer to the nearest integer.

Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.
Question: This is the graph of $y=\sqrt{6 x+7}$, which goes through (-1,1), (3,5), (5,6), (7,7). Use the graph to find an approximate solution to $\sqrt{6 x+7}=6$. Round your answer to the nearest integer.
