Air carrier Captain reported loss of airspeed control due to encountering severe turbulence.

Narrative

Upon coasting in over the West Coast we had numerous Pireps shared on our frequency of moderate turbulence. A Company flight reported a +/- 20 knot wind shift at FL350. That alerted us along with information from WSI that we were about to enter an area of turbulence. Instead of waiting for us to encounter to make the commands over the PA to be seated; I called FA (Flight Attendants) at Door 1 using the interphone. I alerted her that we were entering an area of moderate turbulence that based on information would last about 20 minutes or so and for her to share with the other FA's to take precaution and be seated until we got east of the reported area. I repeated myself twice to make she understood while FA was listening in.East of JAGWA we encountered Severe Turbulence that lasted about 30 seconds. XX 14 first had to flight idle and deploy full speed brake to avoid over speeding. We then encountered a loss of 35 kts. while at max power and speed brake stowed. This all while encountering severe turbulence. Once things settle down; I notified ATC followed by asking the FA's to check in. Via the inter phone I got confirmation that they were all ok. I asked them to check the Cabin to confirm that all passengers were ok. I was notified that a Gentleman had to throw up in the Lavatory at door 2; other than that all passengers were ok and most importantly that we had no injuries to passengers nor crew! We continued our flight to our destination.