The foci of a certain ellipse are at $(3,10 + \sqrt{105})$ and $(3,10 - \sqrt{105}).$  The endpoints of one of the axes are $(-5,10)$ and $(11,10).$  Find the semi-major axis.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
The foci of a certain ellipse are at $(3,10 + \sqrt{105})$ and $(3,10 - \sqrt{105}).$  The endpoints of one of the axes are $(-5,10)$ and $(11,10).$  Find the semi-major axis.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
13
The foci of a certain ellipse are at $(3,10 + \sqrt{105})$ and $(3,10 - \sqrt{105}).$  The endpoints of one of the axes are $(-5,10)$ and $(11,10).$  Find the semi-major axis.
train