How do I sum totals from multiple named worksheets?

Each worksheet is named with a unique client name, such as: John Appleton, Cindy Wilson, Adam Smith etc..
Each worksheet contains a value in cell L3 (actually cells L3 & L4 have been merged).
On a separate worksheet, I'd like to add a formula to a cell that will automatically return a grand total, based on the total appearing in each worksheet.
For example, cell L3 on the sheet named John Appleton could be populated with the number 369, the sheet named Cindy Wilson could have cell L3 populated with the number 872 etc.
Using a calculator at this point may seem practical, but once I have 100 sheets, using a formula would be the only reasonable way to approach this challenge.
Please bear in mind, that worksheets are added/removed all the time, and that some of the values in cell L3, will be altered on some of the sheets, from time to time.
So I really need something super dynamic to handle all the modifications that occur, almost daily.
Please let me know if this can be done with a formula, as I'm really not good with macros.

Thank you

Thank you so much, Richard - works like a charm!