Dummy index automatic summing

https://mathematica.stackexchange.com/a/222410/73364
I have obtained the following code from the above link. But it is not working well with my situation. Can anyone help me out?

SumHeld /: 
  SyntaxInformation[
   SumHeld] = {"LocalVariables" -> {"Table", {2, Infinity}}};

IndexUnify[HoldPattern@Plus[sums : SumHeld[_, __] ..]] := 
 Plus @@ With[{targetIndices = List @@ #[[-1, 2 ;;, 1]], 
      sourceIndicesList = List @@@ #[[;; , 2 ;;, 1]]}, 
     Function[{sum, sourceIndices}, 
       sum /. Thread[
         sourceIndices -> 
          Take[targetIndices, Length@sourceIndices]]] @@@ 
      Transpose@{#, sourceIndicesList}] &@
  SortBy[Flatten /@ {sums}, Length]

SumTogether[HoldPattern@Plus[sums : SumHeld[_, sameRanges__] ..]] := 
 SumHeld[Plus @@ {sums}[[;; , 1]], sameRanges]
SumTogether[HoldPattern@Plus[sums : SumHeld[_, __] ..]] /; 
  UnsameQ @@ {sums}[[;; , 2 ;;]] := 
 Plus @@ SumTogether@*Plus @@@ GatherBy[{sums}, Rest]

Here please see the below test case.

test = SumHeld[f[a, i], {a, 1, 5}, {i, 1, 5}] + 
  SumHeld[SumHeld[2*f[b, j], {b, 1, 5}], {j, 1, 5}] + 
  SumHeld[SumHeld[2*f[c, j], {c, 1, 5}], {j, 1, 5}]
% // IndexUnify
% // SumTogether

The output I am receiving is

$$text{SumTogether}left(sum _{c=1}^5 sum _{j=1}^5 f(c,j)+2 sum _{c=1}^5 sum _{j=1}^5 2 f(c,j)right)$$

Here the issue is it’s not simplifying further as $$left(sum _{c=1}^5 sum _{j=1}^55f(c,j)right)$$

Another question is when I have more than 2 summation signs as below:

test = SumHeld[f[a, i, j], {a, 1, 5}, {i, 1, 5}, {j, 1, 5}] + 
  SumHeld[SumHeld[2*f[b, j, i], {b, 1, 5}, {j, 1, 5}], {i, 1, 5}] + 
  SumHeld[SumHeld[2*f[c, j, i], {c, 1, 5}, {j, 1, 5}], {i, 1, 5}]
% // IndexUnify
% // SumTogether

Is the bracket I have placed correctly?

SumHeld /: c_?NumericQ SumHeld[rest_, range__] := SumHeld[c rest, range]