Why Didn't the USSR Build An X-15?
I like the X-15, it was certainly an amazing airplane, but the truth is there were few benefits to the space program from the X-15.  It was far from a critical or necessary step:


The Mercury space suit was a direct derivative of the BF Goodrich Navy Mark IV, which had been in use for years. It wasn't developed for the X-15
The rockets used in the space program were completely different from the X-15. They were orders of magnitude stronger for one thing, used different fuels and completely different designs. Throttle-able rocket propulsion systems weren't new
The X-15 thermal protection system was of no use to the space program, which had to deal with far higher temperatures 


There were some benefits:


It was a good source of astronauts: several pilot from the program went on to the NASA programs, including Neil Armstrong
Data from the X-15 missions were used in the X-20 Dyna Soar spaceplane which never flew, but it eventually morphed into the space shuttle


As to why didn't the Soviets make one, they didn't need it. Their manned space program built off of their ICBM development efforts which were successful. If the US hadn't built the X-15 the manned space program would most likely never gone the space shuttle route, but that wouldn't have been any sort of deal breaker.