Hi,
To get any further with this your best bet is probably to order this Marriage Cert:
Name: Frank James
Spouse Surname: Jenkins
Date of Registration: Oct-Nov-Dec 1955
Registration district: Pontypridd
Inferred County: Glamorganshire
Volume Number: 8b
Page Number: 965
That will give you Occupations and Addresses, and both Father's names.
You can then check for any children's Births for this couple.
Because of the timescale, and the very common names, the best route then is probably to check Electoral Rolls.
HTH, Romilly.