The problem is that the underlying gdbm library stores mere strings as the value of an entry, not Perl data structures. And the Perl module GDBM_File (which is just a thin wrapper around the library) doesn't provide any automatic serialization/deserialization either.

In other words, you'd have to do that yourself (using Storable, Data::Dumper, whatever) if you want to stick with GDBM.  I.e., convert the Perl data structure into a sequence of bytes (serialization) upon writing, which you'd then have to convert back into a Perl data structure (deserialization) after having read the string from the DB.  Personally, I would rather use another module better suited for the task (like the already mentioned DBM::Deep).