Total Stake Until the First Six

You roll a fair die repeatedly until the first time a 6 appears; let $N$ be the number of rolls (including the winning roll). On each roll you independently collect a payoff $X_i$ with $E[X_i]=1.5$, where the $X_i$ are i.i.d. and independent of the roll values. Compute $E\!\left[\sum_{i=1}^N X_i\right]$.