I know that the total MR = MR of student + MR of adult, but wy is it kinked at the top?
I believe this is just a horizontal sum. At the very top of your graph, only adult has a part of its curve above 10.25. So when your summing horizontally student =0 Adult = x, This changes once you are below 10.25, then all of a sudden you have student = x and adult = x. This additional amount from student causes the kink. If pretend student was always =0 then the total on the right would be identical to adult.
I hope this helped. I'm sorry if it's not phrased better.