My guess would be that if you can manage a 35 mile ride in one go, then a 6.5 mile commute should be easily within your capabilities. However you may need to work up to doing it every day.
I would recommend trying it on a weekend at a comfortable pace to give you an idea of how long it will take, and to familiarise yourself with the route, then try cycling in, say, Monday, Wednesday and Friday (assuming you work Monday-Friday). When that feels comfortable try adding in the extra days until you are comfortable doing the full week.
Remember, it doesn't matter how fast you go, so take your time and enjoy it.
Good luck.