How to sum intermittent cells per cell fill color

[MrDB4Excel]

I have been searching for the better part of 3 hours to find out how to do this, but nothing seems to give an answer that works.
I have a sheet where I want to get a sum of the numeric values in the cells that contain fill colour index #46 (kind of a burnt orange). These cells are intermittent, meaning the first such cell is A284, the next is A311, etc., etc.
I want the sum to appear in Cell A11 which is a cell in my header.
Obviously, I could do this the long drawn out method as in =sum(a284,a311 etc.), adding the next generated such cell as it happens, but I already have many like this and as I continue working in this sheet I will have many more.
This is not a macro-enabled sheet and I do not want it to become macro-enabled, but to remain a simple *.xlsx workbook.
Any help is greatly appreciated.
I have tried SUMIF, setting conditional formatting, and a slew of other attempts at various other functions, but nothing is getting it right.
I obviously am missing something.

 

[MrDB4Excel]

Hello Fluff,
I was a bit premature in saying this was exactly what was needed. I could not get it to work after much trial.
I finally arrived at the solution after considerable testing. Here it is in its entirety prefaced with some comment.

How I Finally Fixed This Problem
The first “A” cell that contains the formula =EXTRACTNUMBERS is A284; therefore the formula in this cell is =EXTRACTNUMBERS(C284). This formula looks at the information in the corresponding “C” column cell, in this case C284 which contains the following text: 9 Lines Translated Today.
This in turns provides the numeric value in A284 of 9. Then I developed 4 helper columns as follows:
These Four Helper Columns may or may not have all been needed, but at this point the end result works perfectly, so these 4 helper columns remain and under no circumstances will I endeavor to fix, alter or change in any way their content.
Column “J” contains the formula: =ISFORMULA(A284)
Column “K” contains the formula: =VALUE(A284)
Column “L” contains the formula: =IF(A284>K284,A284*1)
Column “M” contains the formula: =VALUE(L284)
Cell “M1” contains the formula: =SUMIF(M284:M1411,">0") - SUMIF(M284:M1411,"<0")
Cell “A11” which contains the running total for all the cells in column “A” below cell “A284” which keep track of the “Lines Translated Today” has the simple “=M1” statement.