That looks OK to me (Update: you have an extra closing paren after the second star or else missing the opening one), but I guess you are asking how you can capture the part in parentheses. For that, as sh1tn shows below, you need to use unescaped, plain parentheses around the part you want to capture. Then, the captured stuff will be accessible to you in $1, assuming that there was a match.
in reply to Re^2: data between brackets
in thread data between brackets
In the OP, you say "How do I edit the $value to keep only between the brackets data". If you really mean "edit", then you should use the substitution operator, as sh1tn shows below. You can check perlop for information on it (search within that page for "replacement").
Since this is a problem that many developers often face, there are canned, well-tested regexes that solve it, which also handle nested brackets as a bonus. See Re: regex to parse (nested) parenthesis delimited string? for an example.