My understanding is that most of the translation of Russian to English for scientific purposes was done by the Americans, not by the Soviets. The US devoted relatively huge resources to translation projects in order to keep abreast of Soviet work and advancements. This was, interestingly enough, a major motivation for machine translation research (you can see Google Translate's approaches to doing this as coming out of this original impetus).

Separately, it is worth noting that practically nothing was going to be translated or published by the USSR that was considered to be a major advantage to the West. It was a closed society with very stringent controls of publication and speech. You might ask, instead, why they published abroad at all — why not just keep everything "in house," so to speak? That's a more complicated question about Soviet ideas about the nature of science (they retained some notion of its internationalism, even if they at times went against that), and the degree to which they still desired appreciation from other nations (including but not limited to the West — Soviet science was exported to lots of other countries as well as part of a more "global" Cold War effort; e.g. the Soviets definitely wanted inroads in places like India). There were always limits on sharing (and there were in the US as well — aside from obvious limits like classified research, there is an entirely nebulous area of Export Controls which can apply to even unclassified research).

There were complimentary efforts on the Soviet side of things, translating foreign journal articles (not just English or American) into Russian for domestic consumption.

For lots and lots and lots of details check out Michael Gordin's excellent volume Scientific Babel (2015), which is about the changing languages of science (and it has two chapters that deal specifically with the Russian-English issues in the Cold War, including the mechanical translation discussions).