member "Node::next" (of a friend class) is inaccessible
Solution 1:
A friend declaration grants access of the specified class to the private members of the declaring class (ie, "that class X over there is a friend of mine, he has permission to use my private stuff").
So, by declaring Node as a friend inside of LinkedList, you are granting Node access to LinkedList's private members, not the other way around like you want.
To let LinkedList access Node::next, you need to declare LinkedList as a friend of Node instead:
class Node {
friend class LinkedList;
...
};