Let the random variable $X$ be the number on the first die, and $Y$ be the number onthe second die. We can findthe expected value of the sum using linearity of expectation:$$E [X + Y] = E [X] + E [Y]$$

Now we know that the expectation of a fair die roll is 3.5, so we get:$$E [X + Y]= 3.5+3.5=7$$

This result has nothing to do with independence and holds regardless.