Loading a 32 bit unsigned value into a single mips register

Question

I am currently working a program that runs the Collatz Conjecture. I am confused how to represent 2^32 - 1 or 0xFFFFFFFF into a single register. I am currently using

#lui $s5, 0xFFFF  # 2^32 - 1 stored in $s5
#ori $s5, $s5, 0xFFFF # storing 0xFFFFFFF in $s5
li $s5, 0xFFFFFFFF # pseudo instruction of above
addu $s6, $0, $s5

To get the unsigned value of 0xFFFFFFFF into register $s6. When I run the program through gdb debugger I am getting the 2's complement of 0xFFFFFFFF -1 in register $s6 and not the true unsigned value of 0xFFFFFFFF. I am confused on how to represent the unsigned value of 0xFFFFFFFF into the $s6 register. I am running my code on a ci20 machine not a simulator. Any help or suggestion would be greatly appreciated.