The British have never produced a "Dime" coin.
The "Dime" is a US 10 cent coin.
The value of a dime from 1911 depends on its condition. The lowest a 1911 dime has gone for was $3 and the highest was over $400, however that dime was in mint condition.
The first Mercury design dimes were made in 1916. If your dime is dated 1911 it's a Barber dime, named for its engraver Charles Barber. See the Related Question for more information.
The British didn't make a half dime.
The 1911 Barber dime (not Liberty) is a common date of the series. Retail values for coins in average circulated condition is $2.00-$5.00
If it's a US dime it's referred to as a Barber dime with Lady Liberty on the obverse not Caesar. values are $1.00-$3.00 in average condition
The 1911 US Barber dime is a common coin. A coin in average condition is $2.00-$5.00
$2 if very worn, $5 if only moderately worn, and around $20 if "like new"
A Barber dime dated 1911 in G-4 to VG-8 retails at $2.00-$3.00
1911 is not a rare year for Barber dimes. With no mint mark or a D on the back, its retail value as of 11/2008 is roughly: Very worn condition - $2 Moderately worn - $8 Almost no wear - $50 Uncirculated - $80+ For a coin with an S mint mark, values are approximately double those of a plain or D dime.
Assuming it's circulated and has no mintmark, the 1911 US Barber dime is a common coin. A coin in average condition is $3.00-$5.00.
In order to give an accurate estimate, the coin should be seen. I suggest you take it to a coin dealer and have it appraised.
the value of a dime is ten cents