What is the difference between rvalue and lvalue references to functions?

Question

From c++11 onwards, there are lvalue and rvalue references. I am aware of the differences between them. However, akin to function pointers such as int(*fptr)(), c++ also has lvalue and rvalue references to functions int(&lvalue)() and int(&&rvalue)(), and there doesn't appear to be any difference in this case. What is the difference between them, and when should I use which one?

The following code runs the same thing using lvalue and rvalue references. There doesn't appear to be a difference, and they seem to be able to be used interchangeably as function parameters as well.

#include<cstdio>
int add(int x){return x+1;}
int runLvalue(int(&input)(int),int val){
    return input(val);
}
int runRvalue(int(&&input)(int),int val){
    return input(val);
}
int main()
{
    int(&lval)(int)=add;
    int(&&rval)(int)=add;
    printf("%d %d %d %d %d %d",
        runLvalue(lval,8),
        runRvalue(lval,9),
        runLvalue(rval,0),
        runRvalue(rval,4),
        lval(5),
        rval(1));
    return 1;
}

This outputs 9 10 1 5 6 2 as expected, and doesn't appear to show any reason to use one type of function reference over the other.