Searching sum of constants in a polynomial Consider the polynomial $f(x)=x^3+ax+b$, where $a$ and $b$ are constants. If $f(x+1004)$ leaves a remainder of $36$ upon division by $x+1005$, and $f(x+1005)$ leaves a remainder of $42$ upon division by $x+1004$, what is the value of $a+b$?

HINT: From the given information $$f(x+1004)=36+(x+1005)b_{1}(x)\\
f(x+1005)=42+(x+1004)b_{2}(x)$$
So, $$f(-1)=-a+b-1=36\\
f(1)=a+b+1=42$$
