You will land at the A gates, walk over the bridge to customs/immigration, get dumped into the main terminal on level 5. From there you will have to go up to level 6, re-cleat security and take the train back to either A or B depending on your departing gate. 60 minutes is definitely doable, but it's tight. We regularly make it from the door of the plane to clearing global entry customs/immigration with no checked luggage in under 10 mins. Factor in another 10 minutes (minimum) to re-clear security and get on the train and you are likely already at boarding start time for your connecting flight.

DEN frequently has late afternoon thunderstorms in the summer months that can cause delays. If there is another flight to your destination after the currently scheduled one, it would certainly be safer.