You could have 1 dime, 12 nickels and 930 pennies.
You could have 9 quarters, 24 dimes, 35 nickels and 360 pennies.
You could have 33 quarters, 8 dimes, and 19 nickels.

Many, many, many ways!

Notice thet you didn't say anything about not having other coins
besides nickels and dimes.  You just said there are 11 more nickels 
than dimes.  That is true about all those solutions above, and
there are many other possibilities.  

Be sure to state if the bank only contains nickels and dimes.

If you meant that there are only nickels and dimes, then

Let d = the number of dimes

Then the number of nickels is d+11

The equation comes from

             

          0.05(d+11) + 0.10(d) = 10.00

Clear of decimals by multiplying all the decimals by 100.

                 5(d+11) + 10d = 1000
                 5d + 55 + 10d = 1000
                      15d + 55 = 1000
                           15d = 945
                             d = 63

So there are 63 dimes and 

The number of nickels is d+11 = 63+11 = 74 nickels.

Edwin