SQL & PL/SQL :: Grouping List Of Elements With One Or More Common?

I have a one column table that store lists of elements :

create table test_table (c1 VARCHAR2(4000));
insert into test_table values ('1,23');
insert into test_table values ('1,2');
insert into test_table values ('3,4,5');

[code]...

The output column would be something like that:

output_column
1,2,7,23
6,9,0
3,4,5

I'm grouping columns that have at least one element in common.

(1,23) and (1,2) merge into : (1,2,23)
(1,2,23) and (7,2) merge into : (1,2,7,23) --> Output
(6,9) and (9,0) merge into : (6,9,0) --> Output
(3,4,5) and (5,5) merge into : (3,5,5) --> Output

I have made this logic using only PL/SQL, with loops and nested tables using function memberof, but I suppose that there is a way to improve the performance using only SQL.