Matching brackets in a string

Question

What is the most efficient or elegant method for matching brackets in a string such as:

\"f @ g[h[[i[[j[2], k[[1, m[[1, n[2]]]]]]]]]] // z\"

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Answer 1

Edited (there was an error there)

Is this too naïve?

doubleB[x_String] :=
  StringReplace[
   ToString@StandardForm@
     ToExpression["Hold[" <> x <> "]"], 
  {"Hold[" -> "", RegularExpression["\]\)$"] -> "\)"}];

doubleB["f[g[h[[i[[j[2], k[[1, m[[1, n[2]]]]]]]]]]]"]
ToExpression@doubleB["f[g[h[[i[[j[2], k[[1, m[[1, n[2]]]]]]]]]]]"]

->

Just trying to exploit Mma's own parser ...