We know that a watch gains 7 minutes and 6 seconds every 6 days which means the watch gains $\(7 \times 60+6=420+6=426\)$ seconds in 6 days $\((\because 1$ minute $=60$ seconds $)\)$.

So, the time that the watch gains in 1 day would be $\(\frac{426}{6}=71\)$ seconds $\((=60+11)\)$ which is same as 1 minute and 11 seconds

Hence the answer is (C).