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.