In a large mixing bowl, whisk together root beer, cream, corn syrup, sugar, and vanilla until very well combined. Whisk in salt to taste. The root beer bubbles may form a fizzy raft in the bowl when combined with the cream; this is fine, and churning will fully incorporate it into the base.
If root beer and cream were not chilled, refrigerate mixture for 2 to 3 hours until very cold. Churn mixture according to manufacturer's instructions. Transfer sherbet to container and chill in freezer for at least 3 to 4 hours before serving.
