How can I eradicate bittersweet vine?

Last year I followed the directions of cutting the vines close to the ground so that the vines climbing trees, shrubs and fence would die off. Then I dug and pulled as much root as possible and painstakingly painted the exposed root ends with an herbicide. This process has proven unsuccessful as bittersweet continues to flourish in my yard. There must be an easier way to kill this invasive vine.

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