VBA to select next cell(s) with specific text

I'm working through a large data set that is a bit of a mess. The column I'm trying to deal with has a combination of client numbers and dates:

12684632
12/2/14
1/23/15


368543286
11/3/14
385498651
11/2/14


etc...

I'm trying to figure out a way to find the next cell that contains a date (basically the next cell that contains a /), select it, and select all cells below that also contain a /, stopping when the next cell does not contain a /

e.g. in the figure above starting at the top, the first two dates (12/2/14, 1/23/15) would be selected, then some other vba runs and does its thing (I've got this part working), then selects the next date (11/3/14), etc.

Any help would be really appreciated. Thanks!

Thanks for your help, but this doesn't seem to do anything for me. No error messages, nothing happens if I run it or go step by step. Am I missing something obvious?

Here's a sample of the column I'm dealing with. The data in other columns is more client info. Due to the way the report is run, I can only get this data as plain text, meaning dates are formatted as text. That may be the problem.
sample.xlsm

Thanks to everyone for your input. Mrice, I got it to work. Not sure what the problem was but looks like user error on my end. This has saved me an immense amount of time!