There is only one Rees Parry birth registered in Llandovery between 1850-1860:
1854 Jul Qtr - Vol 11A Page 511
If you purchase his birth certificate that will give you his parents names.
You can purchase his birth certificate from the GRO at http://www.gro.gov.uk/gro/content/certificates/Login.asp
You have the 1911 Census, so that will tell you how long they had been married. When you know that you can search the marriage register for Mary's family name.
Rees and Mary appear in the 1881 census together living at 26, Cobs Slopes, Bedwelty, Monmouthshire. As there are no children, they I would guess they had not long been married. There is a marriage of a Rees Parry in 1880 at Bedwellty, but equally there 4 marriages for a Rees Parry between 1871 and 1881, 2 of which are in Llandovery.
If you identify a marriage based on the information in the 1911 census about how long they had been married, that certificate will identify where they were living when they married, their father's names and occupations, and the marital status of Rees and Mary.
Hope this helps a little.