Expected Sum of Dice Rolls Until a Target Face

You repeatedly roll a fair 6-sided die and keep a running total of every value you roll. The process stops the moment you roll a 1. What is the expected value of the running total at that point (including the final 1)? **Follow-up:** Suppose instead you stop the first time you roll a 6, or any other specific face $k \in \{1, 2, 3, 4, 5, 6\}$. Does the expected total change?