The answer to this all depends on which soldiers you are referring to. If you are just referring to the soldiers within the brigade itself, Tennyson states in every stanza that there are 600 soldiers within the regiment. If you are asking how many soldiers total were involved in the battle that Tennyson is describing, that is a much more difficult question to answer. We know that there were 600 soldiers in the light brigade, but Tennyson never mentions a number for the Russian and Cossack soldiers that are attacking them. He only mentions that the light brigade is completely surrounded with "cannon to the left of them, cannon to the right of them, cannon in front of them."
If you were to ask how many soldiers survived the battle, this is another tough question to answer because Tennyson never gives a clear number. Most of the men are slaughtered, but it is clear that some of them survive because they are seen retreating; "they rode back, but not, not the six hundred." Obviously, some of the light brigade made it out of the battle, but not all of them.