Okay, we are tasked with adding 5819966556 and 2575601100. Let's begin!

Step 1: We'll start by adding the digits 6 & 0 in column 1 and get 6.

Step 2: We'll start by adding the digits 5 & 0 in column 2 and get 5.

Step 3: We'll start by adding the digits 5 & 1 in column 3 and get 6.

Step 4: We'll start by adding the digits 6 & 1 in column 4 and get 7.

Step 5: We'll start by adding the digits 6 & 0 in column 5 and get 6.

Step 6: We'll start by adding the digits 9 & 6 in column 6 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

Step 7: We'll start by adding the digits 9 & 5 in column 7 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

Step 8: We'll start by adding the digits 1 & 7 in column 8 and get 9.

Step 9: We'll start by adding the digits 8 & 5 in column 9 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

Step 10: We'll start by adding the digits 5 & 2 in column 10 and get 8.

So, 5819966556 + 2575601100 = 8395567656.

