Design and implement a linked implementation of a set data structure in Python.

Implement a class called "Node" that represents a single node in the linked set.

Implement a class called "LinkedSet" that represents the set data structure.

add$($value$)$

remove$($value$)$

contains$($value$)$

union$($other$\_$set$)$

intersection$($other$\_$set$)$

The LinkedSet class should be implemented using linked nodes. Do not use any built$-$in data structures like lists or sets to store the values in the set.

Test your implementation by creating several sets and performing various operations on them $($adding elements, removing elements, finding the union and intersection of sets$)$ to ensure that the code is working as expected.