Can you solve this addition problem in your head?

Imagine an addition table for the numbers 1 to 10. The rows and columns are both labeled from 1 to 10 and the entries in the table are row + column. What is the sum of all the entries in the table? You may find it helpful to use the fact that the sum of the numbers from 1 to 10 is 55. When I first thought of this, it seemed rather daunting, but the problem simplifies in a surprising way using some very elementary algebra.